In the Forsaken Outpost, there are two tasks. The first is to collect a pair of books, required for Gibbet. The second task is a simple visit from Effluvium, just passing through enough to also unlock something in Gibbet. If you completed both Bright Crucible and Sacred Grove, you can also access the secret level Desolate Garden.
When you first arrive from the Castle of Grief, you arrive at a dark cave with ettins (and Afrits if playing the Cleric or Mage), and green mana in the eastern path. To the north is a small chasm with Chaos Serpants on the central pillar, and guarding the doors ahead. The visible repulsion disks can be retrieved by walking on the sparkling bridge.
When you open the doors to the outpost, a group of slaughtaurs and centaurs will attack, supported by two chaos serpants at the back.
For the Liber Obsura, you need to reach the other side of the courtward, and turn left. Head to the bottom of the darkened stairs, and pull the switch. This opens a door on the way back, leading to a corridor with the book on a raised platform.
Approaching the book will raise the side walls, causing Dark bishops to attack, as well as teleport one in behind you. The best option is to try to withdraw back into the staircase, using a disk of repulsion if one is blocking, or using your ultimate weapon to clear a defensive position.
In the outpost's courtyard, enter the southeast building to collect the rusty key. If the door to the east is open, you can enter the cave for a porkelator and eight crystal vials, but it is not required.
Proceed through the rusty doors to the north. The following room contains centuars, ettins, and after about 17 seconds, additional enemies will arrive by teleporting or by being freed from the northern corners of the room. You can use your ultimate wepaon to clear out the hordes, and there's plenty of healing items on the sides to recover from damage.
There are four doors in the room, found on the west and east walls. These lead to a subrooms, where you can pull a switch. Pulling all four will open the north wall, where you can retrieve the Daemon Codex. As stated above, if you met the requirements, you can enter the portal to the Desolate Garden.
If you arrived from the effluvium, walk down the middle of the room to trigger a linedef (specifically one between the second and third stained glass windows). This shows a message that a door opened in Gibbet.
The fastest way to Gibbet is to return the way you came, as there should now be a newly opened shortcut in Effluvium. You're still free to continue, opening the door ahead and exploring the cave that contained the eight crystal vials.